State whether the following statement is True or False and justify your answer:
$A$ cone,a hemisphere,and a cylinder stand on equal bases and have the same height. The ratio of their volumes is $1: 2: 3$.

(TRUE) Let the radius of the base of the cone,hemisphere,and cylinder be $r$. Since they stand on equal bases,their radii are equal.
Given that they have the same height,and the height of a hemisphere is equal to its radius $(r)$,the height of the cone and the cylinder must also be $r$.
$1$. Volume of the cone $(V_1)$: $V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^2 (r) = \frac{1}{3} \pi r^3$.
$2$. Volume of the hemisphere $(V_2)$: $V_2 = \frac{2}{3} \pi r^3$.
$3$. Volume of the cylinder $(V_3)$: $V_3 = \pi r^2 h = \pi r^2 (r) = \pi r^3 = \frac{3}{3} \pi r^3$.
Comparing the volumes: $V_1 : V_2 : V_3 = \frac{1}{3} \pi r^3 : \frac{2}{3} \pi r^3 : \frac{3}{3} \pi r^3 = 1 : 2 : 3$.
Thus,the ratio of their volumes is $1 : 2 : 3$. The statement is True.